What happens if you don't take the supplies from the car?

Nothing significant changes.

It doesn't matter if you don't take the supplies by the end of chapter 2, the rest of your group will take them anyway without you (one of will hand Clementine a battery). The stranger will say you took supplies from his car, Lee will respond by saying he didn't take but his group did and the stranger will say Lee didn't do anything to stop them.